Variational phase-field models of fracture have been at the center of a multidisciplinary effort involving a large community of mathematicians, mechanicians, engineers, and computational scientists over the last 25 years or so. I will start with a modern interpretation of Griffith's classical criterion as a variational principle for a free discontinuity energy and will recall some of the milestones in its analysis. Then, I will introduce the phase-field approximation per se and describe its numerical implementation. I illustrate how phase-field models have led to major breakthroughs in the predictive simulation of fracture in complex situations. I then will turn my attention to current issues, including crack nucleation in nominally brittle materials, fracture of heterogeneous materials, and inverse problems.